### Abstract

Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber M_{p} traveling at velocity V through a uniform gaseous medium of density ρ_{0} and sound speed c_{s}. This drag force acts in the direction -V̂ and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion (Script M sign = V/c_{s} > 1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion (Script M sign < 1), the wake is confined to a sphere of radius c_{s}t centered a distance Vt behind the perturber. Inside the wake, surfaces of constant density are hyperboloids or oblate spheroids for supersonic or subsonic perturbers, respectively, with the density maximal nearest the perturber. The dynamical drag force has the form F_{DF} = -I × 4π(GM_{p})^{2}ρ_{0}/V^{2}. We evaluate I analytically; its limits are I → Script M sign^{3}/3 for Script M sign ≪ 1, and I → ln (Vt/r_{min}) for Script M sign ≫ 1. We compare our results to the Chandrasekhar formula for dynamical friction in a collisionless medium, noting that the gaseous drag is generally more efficient when Script M sign > 1, but is less efficient when Script M sign < 1. To allow simple estimates of orbit evolution in a gaseous protogalaxy or proto-star cluster, we use our formulae to evaluate the decay times of a (supersonic) perturber on a near-circular orbit in an isothermal ρ ∝ r^{-2} halo, and of a (subsonic) perturber on a near-circular orbit in a constant-density core. We also mention the relevance of our calculations to protoplanet migration in a circumstellar nebula.

Original language | English (US) |
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Pages (from-to) | 252-258 |

Number of pages | 7 |

Journal | Astrophysical Journal |

Volume | 513 |

Issue number | 1 PART 1 |

DOIs | |

State | Published - Mar 1 1999 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

- Hydrodynamics
- ISM: general
- Shock waves

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## Cite this

*Astrophysical Journal*,

*513*(1 PART 1), 252-258. https://doi.org/10.1086/306858